... of fundamental solutions in the polar coordinate for field and source points and Fourier series for boundary densities are adopted to ensure the exponential convergence. By moving the null-field point to the boundary, singular and hypersingular integrals are transformed to series sums after introducing...

... parallel to the horizontal bounding surfaces at specified elevations or interfaces. Based on half-range Fourier series and the local/global stiffness matrix approach, the mixed boundary-value problem is reduced to a system of coupled singular integral equations of the Cauchy type with kernels formulated...

... are expanded to degenerate kernels based on the separation of field and source points in the fundamental solution. The unknown boundary densities of the circular plates are expressed in terms of Fourier series. It is noted that all the improper integrals are transformed to series sum and are easily calculated...

... for both a welded and a perfectly slipping film/substrate interface. Variation of the stress-free strain through the thickness of the film is considered to be either arbitrary or represented by a Fourier integral, and solutions are presented in the form of a Fourier series in the lateral dimension x...

... the thickness is given by a polynomial in the thickness coordinate and the Poisson’s ratio is assumed to be constant. The Fourier series method is used to reduce the partial differential equations to a pair of ordinary differential equations, which are solved using the Galerkin method. Results for bending...

... and complex Fourier series are used to solve the heat conduction and Navier equations. 23 Oct 2000 08 May 2002 23 01 2003 functionally graded materials thermal stresses temperature distribution Poisson ratio Fourier series heat conduction thermoelasticity Functionally...

... to cyclic loads having any period. The method is based on decomposing the residual stress in Fourier series. The various Fourier coefficients are computed, in an iterative way, by satisfying equilibrium and compatibility at a few time points inside the cycle. The whole numerical procedure is formulated...

... given for a variety of such cases of isotropic plates in 1 . The author is to be commended for his new approach to the important problem of calculation of natural frequencies for anisotropic plates. However, two comments are in order. vibrations anisotropic media Fourier series...

... + A θ ] , where a 0 is the radius of the unperturbed circle and A θ is the radius perturbation magnitude that is represented by a Fourier series expansion. The proposed method in this study is based on the complex variable theory, analytical continuation theorem, and the boundary perturbation technique...

...C. K. Chao, Professor; C. J. Tan, Graduate Student A general analytical solution for the annular problem with a point heat source is provided in this paper. Based upon the method of analytical continuation and the technique of Fourier series expansions, the series solutions of the temperature...